The Middle Ages
Trails
Iconoclasm
First, make sure you know what an icon is.
Not just what a dictionary says, mind you, but what an icon was in the Middle Ages.
Then look for information on the Iconoclasm Controversy (the phrase varies
a bit).
Icons have quite a history in their own right, quite apart from the controversy that surrounded them at one point. You might look for how these things were handled as the Muslims moved in to southeastern Europe. You might follow the development of icons in Russia.
I find the subject interesting because it goes to the heart of what worship is in a Christian setting. As you might guess, that question has been answered in different ways depending on time and place.